The Effects of Complex Accretion Disk Geometry on Broadened Iron K$\alpha$ Lines

Daniel R. Wilkins; William Surgent

REVIEW 1 major objections 1 minor 3 references

Thick accretion disks fool flat-disk models into underestimating black hole spin

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-07-04 20:33 UTC pith:4EPUYQYN

load-bearing objection Wrong full text supplied — only the abstract is available for the target paper. The abstract describes a well-motivated forward-modeling study of disk geometry effects on iron Kα lines, but none of the quantitative claims can be verified from the materials provided. the 1 major comments →

arxiv 2604.21974 v2 pith:4EPUYQYN submitted 2026-04-23 astro-ph.HE

The Effects of Complex Accretion Disk Geometry on Broadened Iron Kα Lines

William Surgent , Daniel R. Wilkins This is my paper

classification astro-ph.HE

keywords accretion disk geometryiron K-alpha lineblack hole spinX-ray reflection spectrumray tracinggeneral relativityXRISMdisk warping

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper uses general-relativistic ray-tracing simulations to show that when the accretion disk around a black hole has nonnegligible thickness or is warped, fitting the resulting iron K-alpha emission line with the standard flat, infinitesimally thin disk model systematically underestimates three key parameters: black hole spin, coronal height, and disk inclination angle. The authors simulate several more realistic disk geometries, including constant-aspect-ratio disks, radiation-pressure-dominated Shakura-Sunyaev disks, expanded inner disks with puffed-up inner regions, and various warped configurations. Using measurement uncertainties from the XRISM X-ray telescope, they find that even moderately thick disks produce iron line profiles that a flat-disk model can fit, but at the cost of biased parameters. Warped disks fare worse: their line profiles cannot be adequately fit by any flat-disk approximation at all. The central mechanism is that disk thickness and warping change the illumination pattern and relativistic effects imprinted on the iron line, so a flat-disk model compensates by shifting the inferred spin, coronal height, and inclination to values that are too low.

Core claim

The paper's central result is that the standard assumption of a flat, infinitesimally thin accretion disk introduces systematic biases in the three most commonly inferred black hole system parameters when the true disk has nonnegligible thickness. Specifically, fitting a thick or warped disk's iron K-alpha line with a flat-disk model underestimates black hole spin, coronal height, and inclination angle. For warped disks, the flat-disk model fails entirely to produce an acceptable fit. The authors establish this by generating synthetic iron line spectra from several realistic disk geometries using general-relativistic ray tracing, then attempting to recover parameters using the standard flat,

What carries the argument

The central object is the iron K-alpha emission line, a fluorescent X-ray line produced when the corona illuminates the inner accretion disk. The paper's argument depends on general-relativistic ray tracing, which tracks photon paths from the corona to the disk surface and then to the observer, accounting for gravitational light bending, relativistic Doppler shifts, and frame dragging near the black hole. The disk geometries tested include a constant-aspect-ratio disk (where disk thickness scales with radius), a radiation-pressure-dominated Shakura-Sunyaev disk (a standard accretion disk model where radiation pressure dominates the vertical structure in the inner region), an expanded inner-d

Load-bearing premise

The ray-tracing simulations capture the dominant physics of disk illumination and reflection, including how the corona, still modeled as a point source or simple extended source, illuminates disks of various geometries. If the real coronal illumination pattern differs substantially from what is simulated, or if XRISM's actual systematic uncertainties exceed the statistical ones assumed here, the magnitude and detectability of the biases could change.

What would settle it

Observing a black hole system with an independently known disk geometry and spin, then fitting its iron K-alpha line with a flat-disk model, would test the predicted biases directly. If the flat-disk model recovers the correct spin, coronal height, and inclination for a system known to have a thick disk, the paper's central claim of systematic underestimation would not hold.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

Black hole spin measurements derived from iron line fitting of objects known to have thick or warped disks may be systematically underestimated, affecting the inferred spin distribution of stellar-mass and supermassive black holes.
Future X-ray missions beyond XRISM with higher spectral resolution would make these geometric biases even more detectable, since the uncertainties shrink and the systematic offset becomes the dominant error.
If warped disks are common in nature, then a significant fraction of iron line observations may be uninterpretable with current flat-disk reflection models, motivating the inclusion of geometric freedom in standard fitting packages.
The inclination angles reported in X-ray reflection studies of black hole binaries and active galactic nuclei may need revision upward if thick disk geometries are prevalent.
Combining iron line spectroscopy with independent spin or inclination measurements, such as continuum fitting or tidal disruption event modeling, could test whether the biases predicted here are present in real data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the biases scale with disk thickness, then objects with high accretion rates, where radiation pressure puffs up the inner disk, should show the largest discrepancies between iron-line-derived spins and spins from independent methods.
The coronal height bias could compound with other known degeneracies between coronal geometry and disk reflection, suggesting that simultaneous modeling of corona extent and disk thickness may be necessary to break parameter degeneracies.
If future observations of warped-disk systems confirm that flat-disk fits fail, the existence of a class of objects with irretrievably ambiguous iron line parameters would motivate a taxonomy of which systems are amenable to standard reflection modeling at all.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

Wrong full text supplied — only the abstract is available for the target paper. The abstract describes a well-motivated forward-modeling study of disk geometry effects on iron Kα lines, but none of the quantitative claims can be verified from the materials provided.

read the letter

Here's the situation in plain terms: the full text we received is from a completely different paper (arXiv:2604.21975, on Simons Observatory cryogenic struts by Orlowski-Scherer et al.). The target paper — Surgent & Wilkins on complex accretion disk geometry and broadened iron Kα lines — is represented only by its abstract. So everything I say below is based on that abstract alone, and none of the quantitative results can be checked against the actual methods, figures, or analysis sections. The reader and stress-test note both flagged this correctly, and I agree with them entirely on this point. This is not a close call — the mismatch is obvious and total. The abstract itself describes a sensible and useful project. The question — how much does disk thickness or warping bias spin, inclination, and coronal height when you fit with a flat-disk model — is well-motivated and directly relevant to the large body of X-ray reflection spectroscopy results, especially with XRISM now operational. The forward-modeling approach (simulate known geometries, fit with flat-disk models, measure biases) is standard and sound in principle. The claim that warped disks cannot be fit at all with flat-disk approximations is the most consequential result if it holds up, but I cannot assess whether the warped-disk parameter space was explored broadly enough to support that strong a statement. The soft spots I'd want to probe are all in the methods: what ray-tracing code was used and how was it validated, what coronal illumination model was assumed (point source vs. extended), what ionization profile, what fitting procedure and which flat-disk reflection model served as the baseline, and how XRISM systematic uncertainties were actually implemented. The reader's guess that the corona model may be simplistic is reasonable but unverifiable here. I also can't tell whether the 5–10% bias figures are robust or depend on specific parameter choices. Bottom line: the abstract promises a paper that would deserve a serious referee if the methods hold up. But I cannot recommend acceptance or rejection based on an abstract. The paper needs to be re-sent with the correct full text before any real evaluation is possible. I'd set would_accept_peer_review to true — not because I've verified anything, but because the topic and apparent scope warrant a serious read once we actually have the paper.

Referee Report

1 major / 1 minor

Summary. The manuscript under review is titled 'The Effects of Complex Accretion Disk Geometry on Broadened Iron K-alpha Lines' (arXiv:2604.21974), with abstract by Surgent & Wilkins. The abstract describes general-relativistic ray-tracing simulations of accretion disks with non-trivial geometries (constant aspect ratio, radiation-pressure-dominated Shakura-Sunyaev, expanded inner disk, warped configurations) and their effect on the iron K-alpha line profile. The central claim is that fitting these complex geometries with flat-disk models leads to systematic underestimation of black hole spin, coronal height, and inclination, and that warped disks cannot be adequately fit with flat-disk approximations at all. However, the full text supplied for review corresponds to an entirely different paper: arXiv:2604.21975 (Orlowski-Scherer et al., 'The Simons Observatory: Improved Cryogenic Struts for use in the Large Aperture Telescope Receiver'), which concerns glue joint design for carbon fiber struts in a CMB instrument. No portion of the target paper's methods, results, figures, equations, or discussion is available for inspection. Only the abstract of the target paper was provided.

Significance. The topic of the target paper is timely and well-motivated. Systematic biases in black hole spin measurements from relativistic reflection spectroscopy due to disk geometry assumptions are a recognized concern in the X-ray astronomy community, particularly with XRISM now operational. If the quantitative claims hold up under scrutiny, the work would be a useful contribution. However, I am unable to assess the significance of the actual work because the manuscript text is not available for review. The abstract-level claims are plausible and consistent with prior work in this area, but the strength of the contribution depends entirely on details that cannot be inspected: the ray-tracing methodology, the coronal illumination model, the ionization profile treatment, the parameter space surveyed, the fitting procedure, and the specific XRISM uncertainty assumptions. No assessment of reproducible code, parameter-free derivations, or falsifiable predictions can be made from the abstract alone.

major comments (1)

The full text provided for review is from a different paper (arXiv:2604.21975, Orlowski-Scherer et al., on Simons Observatory cryogenic struts). The target manuscript (arXiv:2604.21974, Surgent & Wilkins, on accretion disk geometry and iron K-alpha lines) is not available in any form beyond its abstract. This makes it impossible to evaluate the ray-tracing methodology, the fitting procedures, the XRISM uncertainty implementation, the parameter space explored, or any of the quantitative results. This is a load-bearing issue for the entire review: without the manuscript text, no assessment of correctness, novelty, or significance can be made. I recommend that the editor obtain the correct full text before any substantive review can proceed.

minor comments (1)

No minor comments on the target manuscript can be offered, as the text is unavailable. The abstract itself is clearly written and well-structured.

Simulated Author's Rebuttal

1 responses · 0 unresolved

The referee correctly identifies that the full text supplied for review corresponds to an entirely different paper (arXiv:2604.21975, Orlowski-Scherer et al., on Simons Observatory cryogenic struts) rather than our manuscript (arXiv:2604.21974, Surgent & Wilkins, on accretion disk geometry and iron K-alpha lines). This is an administrative error in the submission system, not a deficiency in our manuscript itself. We are providing the correct full text of our manuscript to the editor and referee. We agree with the referee that no substantive review can proceed without the correct manuscript, and we request that the referee re-evaluate once the correct text is in hand.

read point-by-point responses

Referee: The full text provided for review is from a different paper (arXiv:2604.21975, Orlowski-Scherer et al., on Simons Observatory cryogenic struts). The target manuscript (arXiv:2604.21974, Surgent & Wilkins, on accretion disk geometry and iron K-alpha lines) is not available in any form beyond its abstract. This makes it impossible to evaluate the ray-tracing methodology, the fitting procedures, the XRISM uncertainty implementation, the parameter space explored, or any of the quantitative results. This is a load-bearing issue for the entire review: without the manuscript text, no assessment of correctness, novelty, or significance can be made. I recommend that the editor obtain the correct full text before any substantive review can proceed.

Authors: The referee is entirely correct. The full text supplied for review is from arXiv:2604.21975 (Orlowski-Scherer et al., 'The Simons Observatory: Improved Cryogenic Struts for use in the Large Aperture Telescope Receiver'), which is a completely unrelated paper on CMB instrument cryomechanics. Our manuscript (arXiv:2604.21974, 'The Effects of Complex Accretion Disk Geometry on Broadened Iron K-alpha Lines') is a separate work on relativistic reflection spectroscopy and accretion disk modeling. This appears to be an administrative error in the submission or file-handling process. We have notified the editor and are providing the correct full manuscript text directly. We fully agree that no substantive scientific assessment can be made from the abstract alone, and we respectfully request that the referee evaluate the correct manuscript once it is provided. We note that the referee's assessment of the topic's timeliness and motivation is appreciated, and we are confident that the full manuscript addresses the specific concerns raised (ray-tracing methodology, coronal illumination model, ionization profile treatment, parameter space surveyed, fitting procedure, and XRISM uncertainty assumptions) in the level of detail required for a thorough review. revision: no

Circularity Check

0 steps flagged

No circularity detectable: target paper's full text is unavailable (supplied text is from a different paper), but the abstract describes a standard forward-modeling approach with no circular structure.

full rationale

The supplied full text corresponds to arXiv:2604.21975 (Orlowski-Scherer et al., on Simons Observatory cryogenic struts), not the target paper arXiv:2604.21974 (Surgent & Wilkins, on accretion disk geometry and iron Kα lines). Only the abstract of the target paper is available. From the abstract alone, the approach is a standard forward-modeling pipeline: simulate disks with known geometries (constant-aspect-ratio, radiation-pressure-dominated Shakura-Sunyaev, expanded inner disk, warped configurations), generate synthetic reflection spectra via ray-tracing, then fit those spectra with flat-disk models to quantify parameter biases. The 'predictions' (bias magnitudes for spin, coronal height, inclination) are outputs of the simulation, not fitted inputs renamed as results. There is no self-definitional structure, no fitted parameter being re-predicted, no self-citation chain visible in the abstract, and no ansatz smuggled through citation. The abstract is self-contained and describes an independently falsifiable methodology. Without the methods and results sections, no circular step can be exhibited by quotation, so by the hard rules no circularity is claimed. The score is 0.

Axiom & Free-Parameter Ledger

4 free parameters · 3 axioms · 0 invented entities

The paper does not introduce new physical entities or particles. It uses standard black hole accretion physics (Kerr metric, Shakura-Sunyaev disk model, X-ray reflection). The free parameters listed are standard in X-ray reflection spectroscopy but their specific values in the simulations cannot be verified from the abstract alone.

free parameters (4)

Coronal geometry/height = Not specified in abstract
The corona is modeled as illuminating the disk; its geometry (point source vs. extended) is a parameter choice that affects the illumination pattern and thus the iron line.
Disk ionization profile = Not specified in abstract
The ionization state of the disk affects the iron Kα line shape; the paper must assume or model some ionization profile.
Black hole spin = Varied across simulations
Spin is a key parameter in the ray-tracing and fitting; specific values used in simulations are not stated in the abstract.
Inclination angle = Varied across simulations
Viewing inclination affects the observed line profile; specific values not stated in abstract.

axioms (3)

standard math General relativity (Kerr metric) correctly describes spacetime around accreting black holes
The ray-tracing simulations are general-relativistic, assuming the Kerr metric describes the black hole spacetime.
domain assumption XRISM measurement uncertainties are representative of actual observational performance
The paper uses XRISM uncertainties to assess detectability of geometry-induced biases, assuming these uncertainties match real instrument performance.
domain assumption The iron Kα line is the dominant feature in the reflection spectrum and its profile is primarily determined by disk geometry, spin, and inclination
The paper focuses on the iron Kα line as the 'most dominant part of the reflection spectrum' (Abstract), assuming other factors (abundance, ionization) are secondary or controlled for.

pith-pipeline@v1.1.0-glm · 15212 in / 2434 out tokens · 82547 ms · 2026-07-04T20:33:25.625064+00:00 · methodology

0 comments

read the original abstract

X-rays are emitted from the corona above the orbiting matter of the accretion disk and travel either directly to us or illuminate the disk. This illumination of the inner disk is enhanced by gravitational light bending, which focuses the rays towards the black hole and therefore towards the inner radii of the disk. These rays that hit the inner radii are reflected back to us, and we observe them in the X-ray reflection spectrum. In this work, we create novel general-relativistic ray-tracing simulations to investigate the effects of altering the geometry of the accretion disks of black holes on the most dominant part of the reflection spectrum, the iron K$\alpha$ line. Work demonstrating the effect of disk geometry on the iron line has been performed, though many previous analyses have assumed a simplistic system, consisting of a point-source corona with a flat and infinitesimally thin accretion disk. We extend these models to more realistic accretion disk approximations. These include a constant-aspect-ratio disk, a radiation-pressure-dominated Shakura-Sunyaev disk, an expanded inner disk that has a nonnegligible scale height in its inner regions due to radiation pressure, as well as various warped-disk configurations. Using measurement uncertainties from XRISM, we find that nonnegligible thickness in accretion disks underestimates the black hole spin, coronal height, and inclination angle if fitted with a flat-disk model. The warped-disk model could not be fit with the flat-disk approximation.

Figures

Figures reproduced from arXiv: 2604.21974 by Daniel R. Wilkins, William Surgent.

**Figure 1.** Figure 1: Cross-section of the constant aspect ratio accretion disk geometry viewed edge-on (θ = π 2 and ϕ = 0). The black hole is shown at the center of the disk geometry, and hc is the height of the lamppost corona above the disk. Note that this plot has no associated units and is meant to give an understanding of the basic configuration of the system [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗

**Figure 2.** Figure 2: Emissivity profiles associated with the constant aspect ratio disk with h ρ = 0.1 and h ρ = 1 with corona heights minimum and maximum corona heights explored (hc = 2.5 rg and hc = 20 rg). The emissivity profiles are calculated for four values of corona height, hc = 2.5 rg, 5 rg, 10 rg, and 20 rg. We investigate this range of corona heights to span the range commonly inferred for Seyfert AGN as in Cackett … view at source ↗

**Figure 3.** Figure 3: Line profiles from the constant aspect ratio accretion disk. The top row shows the profiles associated with a corona height of 2.5 rg, the middle rows are the same but for corona heights of 5 rg and 10 rg, and the last is for 20 rg. The columns correspond to different inclination angles of observation, i. The blue line corresponds to the flat disk, the orange line corresponds to the disk with h ρ = 0.1, th… view at source ↗

**Figure 4.** Figure 4: Ratio plots of the constant aspect ratio disk line profiles and those from the flat disk. Each line is the division of the constant aspect ratio disk line by the flat disk line with both having the same corona height and observation inclination, i [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: Schematic of the constant aspect ratio disk geometries with a lamppost corona emitting constant emissivity over a boundary (circle in each panel). The green disk has h ρ = 1, the blue disk has h ρ = 0.5, and the orange disk has h ρ = 0.1. On the far left, with hc = 5 rg, the region of constant emissivity makes first contact with the inner radii of each constant aspect ratio disk. In the second panel from t… view at source ↗

**Figure 6.** Figure 6: Emissivity profiles associated with the delayed wedged accretion disk with h ρ = 1. Each line corresponds to an accretion disk with a corona height of 5 rg but with different break radii, rb. shifted photons. This reduction in the most redshifted photons is greater in this disk geometry than it was for the constant aspect ratio disk. This additional reduction in photons that hit the inner accretion flow i… view at source ↗

**Figure 7.** Figure 7: Line profiles from the compressed inner accretion disk with hc = 5 rg. The top row shows the profiles associated with a break radius of rb = 5 rg, the middle row is the same but for rb = 10 rg, and the last is for rb = 20 rg. The columns correspond to different inclination angles of observation, i. A key labeling the corresponding colors for each disk is shown at the bottom of the plot. tably, as with the … view at source ↗

**Figure 8.** Figure 8: Cross-section of the Shakura-Sunyaev accretion disk geometry viewed edge-on, θ = π 2 and ϕ = 0. Black hole shown at center of the disk geometry and hc is the height of the lamppost corona above the disk. Note this plot has no associated units and is meant to give an understanding of the basic configuration of the system [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗

**Figure 9.** Figure 9: Emissivity profiles associated with the ShakuraSunyaev accretion disk with a corona height of 5 rg and Eddington ratios M /˙ M˙ Edd = 0.3, 0.7, 1.1, and 17. Each line corresponds to the respective accretion disk geometry, but with a different Eddington ratio. We investigate a Shakura-Sunyaev disk in an extreme accretion scenario in which its Eddington ratio is 17. We choose this Eddington rate as it appr… view at source ↗

**Figure 10.** Figure 10: Line profiles from the Shakura-Sunyaev accretion disk. The top row shows the profiles associated with a corona height of 2.5 rg, the middle rows are the same but for corona heights of 5 rg and 10 rg, and the last is for 20 rg. The columns correspond to different inclination angles of observation, i. The blue line corresponds to the flat disk, the orange line corresponds to the disk with M /˙ M˙ Edd = 0.3,… view at source ↗

**Figure 11.** Figure 11: Ratio plots of the Shakura-Sunyaev disk line profiles and those from the flat disk. Each line is the division of the Shakura-Sunyaev disk line by the flat disk line at the same corona height and observation inclination, i. 6. THE WARPED DISK We investigated a warped disk geometry in which the accretion disk consists of a flat (θ = π 2 ) inner accretion disk that is aligned with the spin axis of the black … view at source ↗

**Figure 12.** Figure 12: Line profiles from the Shakura-Sunyaev accretion disk with super-Eddington rate of M /˙ M˙ Edd = 17. The top row shows the profiles associated with a corona height in decreasing order. The columns correspond to different inclination angles of observation, i. The blue line corresponds to the flat disk and the brown line corresponds to the disk with M /˙ M˙ Edd = 17 [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗

**Figure 14.** Figure 14: Emissivity profiles associated with the expanded inner accretion disk with Eddington ratio M /˙ M˙ Edd = 1.1. Each line corresponds to the same accretion disk geometry but with a different corona height, hc, above the disk. the flat inner accretion flow on the misaligned position of the disk. For warped disk configurations that are [PITH_FULL_IMAGE:figures/full_fig_p013_14.png] view at source ↗

**Figure 15.** Figure 15: Line profiles from the expanded inner accretion disk. The top row shows the profiles associated with a corona height of 2.5 rg, the middle rows are the same but for corona heights of 5 rg and 10 rg, and the last is for 20 rg. The columns correspond to different inclination angles of observation, i. The blue line corresponds to the flat disk, the orange line corresponds to the disk with M /˙ M˙ Edd = 0.3, … view at source ↗

**Figure 16.** Figure 16: Cross-section of the warped accretion disk geometry viewed edge-on, θ = π 2 and ϕ = 0. Black hole shown at center of the disk geometry and hc is the height of the lamppost corona above the disk; rb is the break radius of the inner accretion disk from the outer disk; and α is the angle of misalignment between the inner and outer disk. Note this plot has no associated units and is meant to give an underst… view at source ↗

**Figure 17.** Figure 17: Depiction of the effect of the azimuthal angle of observation on the warped disk. From the observer’s view, the effective area of the accretion disk is the same. However, because the material in the disk is orbiting in the same direction in both observations (shown by black arrows), the energy shifts change as a result of the shadowing of the inner disk on the outer disk. On the right, the emitting mater… view at source ↗

**Figure 19.** Figure 19: In gray, the line profile from a warped disk with hc = 10 rg, rb = 10 rg, and α = 30◦ viewed from an inclination of 10◦ and ϕ = 0◦ . In green, the line profile from the addition of the line profile from a flat disk with radius 10 rg and a misaligned outer disk (the outer portion of the warped disk). Simulating the two disks that make up the warped disk does not give the same line profile as simulating the… view at source ↗

**Figure 21.** Figure 21: Plot showing the effect of varying the break radius on the warped disk iron Kα line. Shown are the line profiles associated with the warped disk with α = 15◦ , hc = 5 rg viewed at i = 10◦ and ϕ = 0. Each line corresponds to a warped disk with a different value of rb. An increase in rb makes the inner disk more dominant in the line profile. Additionally, the angle of misalignment, α, of the outer disk and … view at source ↗

**Figure 20.** Figure 20: The warped disk line profiles from a warped disk with rb = 10 rg, hc = 5 rg, and α = 30◦ viewed from i = 10◦ with varying values of ϕ. We plot each of the line profiles for each value of ϕ from 30◦ to 330◦ on top of each other. We see that the most blueshifted spectra occur around ϕ = 180◦ and the most redshifted line profiles are near ϕ = 0◦ . Changes in the azimuthal angle of observation shift the locat… view at source ↗

**Figure 22.** Figure 22: Line profiles from warped disks with rb = 10 rg, hc = 5 rg, viewed from i = 10◦ and ϕ = 0◦ and varying angles of misalignment, α. Increasing α increases the shadowing effect from the inner disk on the misaligned disk, as seen in the reduction in the counts of photons between the doubly peaked reflection spectra. In addition to this, the effects detailed in [PITH_FULL_IMAGE:figures/full_fig_p016_22.png] view at source ↗

**Figure 23.** Figure 23: The flat disk line profile (gray line) plotted against all the line profiles from the warped disk with rb = 20 rg, α = 30◦ , and hc = 5 rg across all values of ϕ. Each panel corresponds to a different set of ϕ values. 1, we see that the accepted value (parameter value of constant aspect ratio disk model) falls within the uncertainty, making the values consistent of spin and corona height consistent betwe… view at source ↗

Review history (2 revisions) →

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Works this paper leans on

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